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Abstract

We use a layered model of normal human skin based on size distributions of polydisperse spherical particles and their complex refractive indices to compute the Stokes scattering matrix at wavelengths in the visible spectral band. The elements of the Stokes scattering matrix are required in a polarized radiative transfer code for a coupled air–tissue system to compute the polarized reflectance and examine how it is dependent on the vertical structure of the inherent optical properties of skin, including the phase matrix. Thus, the elements of the Stokes scattering matrix can be useful for investigating polarization-dependent light propagation in turbid optical media, such as human skin tissue.

References

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Table 1.

Input Variables Used to Calculate the Stokes Scattering Matrix for Four Different Human Skin Layersa

—

U. Epidermis

L. Epidermis

Dermis

Subcutis

—

r1,u=40nm

r1,ℓ=47nm

r1,d=87nm

r1,s=132nm

—

r2,u=359nm

r2,ℓ=735nm

r2,d=1793nm

r2,s=247nm

—

r¯g,u=119.7nm

r¯g,ℓ=185.4nm

r¯g,d=395.0nm

r¯g,s=180.8nm

—

σg,u=1.442

σg,ℓ=1.582

σg,d=1.656

σg,s=1.110

λ0 [nm]

m′+m′′×10−3

m′+m′′×10−3

m′+m″×10−3

m′+m′′×10−3

368

1.559+i5.561

1.521+i4.177

1.493+i2.021

1.580+i0.3915

403

1.560+i4.374

1.523+i3.253

1.502+i6.297

1.576+i0.3483

510

1.561+i2.303

1.527+i1.680

1.486+i0.579

1.570+i0.2574

579

1.563+i1.698

1.528+i1.227

1.490+i1.427

1.568+i0.2181

632

1.563+i1.377

1.529+i0.990

1.493+i0.074

1.567+i0.1945

ar¯g and the σg are respectively the geometric mean radius and the standard deviation of a log-normal distribution of homogeneous spherical particles. The parameters r1 and r2 are respectively the largest and smallest radii of the particles, which are embedded in a nonabsorbing host medium of constant refractive index equal to 1.36 [55]. λ0 [nm] is the wavelength of light in air.

a These values were obtained from a BOM, from Mie calculations (Mie) according to Bhandari et al. [55], and from the T-matrix method (T-matr.) computed using Mishchenko’s T-matrix method [46]. Note that τ˜ (BOM), ω˜ (BOM), and the values of τ˜ (Mie) inside parentheses include contributions from Rayleigh scattering with scattering coefficients μR(λ0) that are the same for all four layers. In units of mm−1, μR(λ0) is 10.9060 for λ0=368nm, 7.5829 for λ0=403nm, 2.9565 for λ0=510nm, 1.7797 for λ0=579nm, and 1.2537 for λ0=632nm.

Tables (2)

Table 1.

Input Variables Used to Calculate the Stokes Scattering Matrix for Four Different Human Skin Layersa

—

U. Epidermis

L. Epidermis

Dermis

Subcutis

—

r1,u=40nm

r1,ℓ=47nm

r1,d=87nm

r1,s=132nm

—

r2,u=359nm

r2,ℓ=735nm

r2,d=1793nm

r2,s=247nm

—

r¯g,u=119.7nm

r¯g,ℓ=185.4nm

r¯g,d=395.0nm

r¯g,s=180.8nm

—

σg,u=1.442

σg,ℓ=1.582

σg,d=1.656

σg,s=1.110

λ0 [nm]

m′+m′′×10−3

m′+m′′×10−3

m′+m″×10−3

m′+m′′×10−3

368

1.559+i5.561

1.521+i4.177

1.493+i2.021

1.580+i0.3915

403

1.560+i4.374

1.523+i3.253

1.502+i6.297

1.576+i0.3483

510

1.561+i2.303

1.527+i1.680

1.486+i0.579

1.570+i0.2574

579

1.563+i1.698

1.528+i1.227

1.490+i1.427

1.568+i0.2181

632

1.563+i1.377

1.529+i0.990

1.493+i0.074

1.567+i0.1945

ar¯g and the σg are respectively the geometric mean radius and the standard deviation of a log-normal distribution of homogeneous spherical particles. The parameters r1 and r2 are respectively the largest and smallest radii of the particles, which are embedded in a nonabsorbing host medium of constant refractive index equal to 1.36 [55]. λ0 [nm] is the wavelength of light in air.

a These values were obtained from a BOM, from Mie calculations (Mie) according to Bhandari et al. [55], and from the T-matrix method (T-matr.) computed using Mishchenko’s T-matrix method [46]. Note that τ˜ (BOM), ω˜ (BOM), and the values of τ˜ (Mie) inside parentheses include contributions from Rayleigh scattering with scattering coefficients μR(λ0) that are the same for all four layers. In units of mm−1, μR(λ0) is 10.9060 for λ0=368nm, 7.5829 for λ0=403nm, 2.9565 for λ0=510nm, 1.7797 for λ0=579nm, and 1.2537 for λ0=632nm.